SpectralToolbox.Spectral1DΒΆ
Functions
AlmostEqual (a, b) |
b = AlmostEqual(a,b) |
BarycentricWeights (x) |
BarycentricWeights(): Returns a 1-d array of weights for Lagrange Interpolation |
FirstPolynomialDerivativeMatrix (x) |
PolynomialDerivativeMatrix(): Assemble the first Polynomial Derivative Matrix using matrix multiplication. |
LagrangeInterpolate (x, f, xi) |
LagrangeInterpolate(): Interpolate function values f from points x to points xi using Lagrange weights |
LagrangeInterpolationMatrix (x, w, xi) |
LagrangeInterpolationMatrix(): constructs the Lagrange Interpolation Matrix from points x to points xi |
LinearInterpolationMatrix (x, xi) |
LinearInterpolationMatrix(): constructs the Linear Interpolation Matrix from points x to points xi |
LinearShapeFunction (x, xm, xp, xi) |
Hat function used for linear interpolation |
PolynomialDerivativeMatrix (x, k) |
PolynomialDerivativeMatrix(): Assemble the Polynomial k -th Derivative Matrix using the matrix recursion. |
SPcomb (N, k[, exact, repetition]) |
The number of combinations of N things taken k at a time. |
SparseLinearInterpolationMatrix (x, xi) |
LinearInterpolationMatrix(): constructs the Linear Interpolation Matrix from points x to points xi . |
SparseLinearShapeFunction (x, xm, xp, xi) |
Hat function used for linear interpolation. |
TestOrthogonality (V, w) |
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cc (N[, norm]) |
cc(): function for generating 1D Nested Clenshaw-Curtis [-1,1] |
factorial (n[, exact]) |
The factorial function, n! = special.gamma(n+1). |
fej (N[, norm]) |
fej(): function for generating 1D Nested Fejer’s rule [-1,1] |
gqn (N) |
GQN(): function for generating 1D Gaussian quadrature for integral with Gaussian weight (Gauss-Hermite) |
gqu (N[, norm]) |
GQU(): function for generating 1D Gaussian quadrature rules for unweighted integral over [-1,1] (Gauss-Legendre) |
kpn (N) |
KPN(): function for generating 1D Nested rule for integral with Gaussian weight |
kpu (N[, norm]) |
KPU(): function for generating 1D Nested rule for unweighted integral over [-1,1] |
nestedgauss (N[, norm]) |
nestedgauss(): function for generating 1D Nested rule for integral with Uniform weight with 2**l scaling |
nestedlobatto (N[, norm]) |
nestedlobatto(): function for generating 1D Nested rule for integral with Uniform weight with 2**l scaling |
Classes
Fourier () |
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GenericOrthogonalPolynomial (mu, endl, endr) |
Construction of polynomials orthogonal with respect to a generic measure |
HermitePhysicistsFunction () |
Construction of the Hermite Physiticists’ functions |
HermitePhysicistsPolynomial () |
Construction of the Hermite Physicists’ polynomials |
HermiteProbabilistsFunction () |
Construction of the Hermite Probabilists’ functions |
HermiteProbabilistsPolynomial () |
Construction of the Hermite Probabilists polynomials |
JacobiPolynomial (alpha, beta[, span]) |
Construction of Jacobi polynomials |
LaguerreFunction (alpha) |
Construction of the Laguerre functions |
LaguerrePolynomial (alpha) |
Construction of Laguerre polynomials |
OrthogonalBasis () |
This is an abstract class for 1-d orthogonal basis |
OrthogonalPolynomial () |
This is an abstract class for 1-d polynomials |
Poly1D (poly, params[, sdout]) |
Initialization of the Polynomial instance. |